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PHY 201
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The equilibrant of a force is the force which is equal and opposite to that force. If two forces are equal and opposite, their x and y components are also equal, but the x and y components of the force are opposite in sign to those of the equilibrant.
The x and y components of a force are 2 Newtons and 3 Newtons repectively.
• What are the magnitude of this force and what angle does it make as measured counterclockwise from the positive x axis? #$&*
magnitude = sqrt(2^2 + 3^2) = 3.6 N
direction of angle = tan^-1 (3 / 2) = 56.3 degree
• What are the components of the equilibrant force? #$&*
x = -2 N
y = -3 N
mag = sqrt((-2)^2 + (-3)^2) = 3.6 N
• What angle does the equilibrant force make as measured counterclockwise from the positive x axis? #$&*
theta = tan^-1 (-3 / -2) = 56.3
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7 mins
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56.3 degrees is a first-quadrant angle, and is in fact the angle of the original vector. So it can't be the angle of the equilibriant, which must be in the opposite quadrant.
The formula for the angle is
theta = tan^-1 ( F_y / F_x), plus 180 deg if F_x is negative.
What therefore is the angle?
I expect it will take you only a minute or so to revise this.
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